The couple had been together for 54 years
The deaths of British conductor Sir Edward Downes and his wife, Joan, have reopened the assisted suicide debate.
Sir Edward, 85, who was losing his sight and hearing, died on Friday alongside his terminally ill wife, 74, at Swiss right-to-die centre, Dignitas.
In a statement, their family said the couple "died peacefully, and under circumstances of their own choosing".
The Metropolitan Police said it was investigating, as campaigners called for more safeguards to be put in place.
Last week, a proposal by Lord Falconer to allow people to help someone with a terminal illness travel to a country where assisted suicide is legal was thrown out by the Lords.
Sarah Wootton, chief executive of Dignity in Dying, said: "This problem is clearly not going to go away; we are descending down a slippery slope towards unregulated assisted dying abroad, at a rapid pace."
She added that people should be able to make decisions about death for themselves but warned that without safeguards, the process was "dangerous and open to abuse".
Peter Saunders, from Care Not Killing, said the Downes' case was "sad but unusual".
He added that the current law was clear and right and the House of Lords was wise not to approve any change to it.
"With imminent health cuts, growing numbers of elderly people and increasing levels of elder abuse the very last thing we need is to put vulnerable people, many of whom already think they are a financial or emotional burden to relatives, carers and the state, under pressure to end their lives through a change in the law," he said.
The Downes are not the first couple to die together at the Swiss centre.
In 2003, Dignitas doctors helped Robert and Jennifer Stokes, of Leighton Buzzard in Bedfordshire, to die.
An inquest a year later heard they had both suffered with mental and physical illnesses over 30 years but neither were terminally ill.
The centre has been criticised in the past for accepting people who are not necessarily terminally ill.
Last year, the centre helped 23-year-old Daniel James commit suicide after he was paralysed playing rugby.
Dignitas has helped more than 115 people from the UK to commit suicide since it was founded in 1998.
None of those cases involved criminal charges, but many were investigated by police.
Assisting a suicide is illegal in Britain under the Suicide Act and carries a maximum sentence of 14 years imprisonment in England and Wales.
A spokesman for the Metropolitan Police said the Downes' deaths were being investigated by Greenwich CID.
"It was reported to police on Monday, July 13, that a man and woman from SE3 had died in Switzerland," he added.
Their son and daughter, Caractacus and Boudicca, said in a statement: "After 54 happy years together, they decided to end their own lives rather than continue to struggle with serious health problems."
Sir Edward, who had a 40-year relationship with the BBC Philharmonic Orchestra, was "almost blind and increasingly deaf", according to his family.
Joan Downes, a ballet dancer and later a choreographer and TV producer, was said to be terminally ill with cancer.
"They both lived life to the full and considered themselves to be extremely lucky to have lived such rewarding lives, both professionally and personally," their family said.
"Our parents had no religious beliefs and there will be no funeral," they added.
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